The quest for fast image acquisition speed has always been a perennial topic in the MRI community. To reduce the acquisition time for maximal spatial and temporal resolution, modern MRI protocols usually perform reduced acquisitions below the Nyquist rate. The reduced data is then used to reconstruct the image through advanced reconstruction techniques that leverage some prior information about the MRI system (e.g., parallel imaging) and/or MR signal (e.g., compressed sensing). Since such prior information is patient and system specific, recent techniques obtain the prior information using training data obtained through an empirical calibration procedure. All existing methods assume the prior models are linear. Since the intrinsic nonlinear relationship in the training data cannot be characterized in such simple models, the reconstruction is degraded by the inaccuracy of the prior information. Nonlinear learning from the training data have proven to be more powerful in machine learning because it is more general and includes the linear model as a special case. However, it is usually more challenging to learn the nonlinear models and even more challenging to incorporate the model in reconstruction due to the increased degree of freedom. We recently have introduced a novel concept of kernel in MR reconstruction to address the above challenges timely. Our preliminary results on parallel imaging and sparsity-constrained reconstruction demonstrate that the kernel-based algorithms improve the reconstruction quality over the original algorithms with linear prior models. Built upon our strong preliminary results, the objective of this application is to develop an innovative kernel-based framework for MR image reconstruction from undersampled data. This framework does not require explicit knowledge of nonlinear mapping (as in preliminary work) such that a broader family of nonlinear functions can be explored for different clinical applications. The proposed work is expected to advance the field of MR image reconstruction vertically. Specifically, the successful completion of the proposed project will result in a general framework leading to many new algorithms (including two developed in this project) for reconstruction from reduced acquisition. Therefore, virtually all of current clinical MRI could benefit from the improved resolution, image quality, and/or reduced acquisition times that the new framework will facilitate or the novel applications i may enable.